Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0)
The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbatio...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/575964 |
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| author | Jing Li |
| author_facet | Jing Li |
| author_sort | Jing Li |
| collection | DOAJ |
| description | The nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples. |
| format | Article |
| id | doaj-art-6a70d31632454a8ea58e0b88b90a40d6 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-6a70d31632454a8ea58e0b88b90a40d62025-02-03T01:30:48ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/575964575964Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0)Jing Li0School of Mathematics and Statistics, Shandong University, Weihai, Weihai 264209, ChinaThe nonlinear matrix equation X-A*X-pA=Q with p>0 is investigated. We consider two cases of this equation: the case p≥1 and the case 0<p<1. In the case p≥1, a new sufficient condition for the existence of a unique positive definite solution for the matrix equation is obtained. A perturbation estimate for the positive definite solution is derived. Explicit expressions of the condition number for the positive definite solution are given. In the case 0<p<1, a new sharper perturbation bound for the unique positive definite solution is derived. A new backward error of an approximate solution to the unique positive definite solution is obtained. The theoretical results are illustrated by numerical examples.http://dx.doi.org/10.1155/2013/575964 |
| spellingShingle | Jing Li Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) Abstract and Applied Analysis |
| title | Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) |
| title_full | Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) |
| title_fullStr | Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) |
| title_full_unstemmed | Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) |
| title_short | Solutions and Improved Perturbation Analysis for the Matrix Equation X-A*X-pA=Q (p>0) |
| title_sort | solutions and improved perturbation analysis for the matrix equation x a x pa q p 0 |
| url | http://dx.doi.org/10.1155/2013/575964 |
| work_keys_str_mv | AT jingli solutionsandimprovedperturbationanalysisforthematrixequationxaxpaqp0 |